Classical limit of non-Hermitian quantum dynamics - a generalised canonical structure

Abstract

We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion, for both conservative and dissipative motion. The dynamical equations combine a symplectic flow associated with the Hermitian part of the Hamiltonian with a metric gradient flow associated with the anti-Hermitian part of the Hamiltonian. We derive this structure of the classical limit of quantum systems in the case of a Euclidean phase space geometry. As an example we show that the classical dynamics of a damped and driven oscillator can be linked to a non-Hermitian quantum system, and investigate the quantum classical correspondence. Furthermore, we present an example of an angular momentum system whose classical phase space is spherical and show that the generalised canonical structure persists for this nontrivial phase space geometry.

19 pages, 5 figures

References in corpus (13)

• Making Sense of Non-Hermitian Hamiltonians
• Visualization of Branch Points in PT-Symmetric Waveguides
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
• Asymmetric scattering and non-orthogonal mode patterns in optical micro-spirals
• Fractal Weyl laws for chaotic open systems
• Semiclassical structure of chaotic resonance eigenfunctions
• Complexified Dynamical Systems
• Bifurcations in Resonance Widths of an Open Bose-Hubbard Dimer
• Many-body interband tunneling as a witness for complex dynamics in the Bose-Hubbard model
• Many-body Landau-Zener tunneling in the Bose-Hubbard model
• Resonance distribution in open quantum chaotic systems
• Geometric dissipation in kinetic equations

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